Preliminary Topology Optimization of Small Unmanned ...

UNIVERSIDADE DA BEIRA INTERIOR Engenharia

Preliminary Topology Optimization of Small

Unmanned Aircraft Wings for Additive

Manufacturing

Cátia Alexandra Louro Miguel

Dissertação para obtenção do Grau de Mestre em

Engenharia Aeronáutica

(ciclo de estudos integrado)

Orientador: Prof. Doutor Pedro Vieira Gamboa

Covilhã, fevereiro de 2019

Preliminary Topology Optimization of Small Unmanned Aircraft Wings for Additive Manufacturing

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“A person who never made a mistake never tried anything new.”

Albert Einstein


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Acknowledgements

I would like to thank all the people that accompanied me through this journey and made me a

better person.

First, I would like to thank my supervisor Pedro Vieira Gamboa, for all the guidance, support

and patience throughout this work. His motivation was essential for the accomplishment of the

work.

Secondly to Pedro Alves and Pedro Carneiro for the advice and help through this work.

I would also thank my friends who, over these years, shared with me good moments and I will

always keep with me. Thank you to André, António, Bruna, Cátia, Daniel, Flávia, Francisco,

Gabriel, Inês, João Miguel, João Rocha, Luís Coelho, Luís Oliveira, Mara, Nicole, Nídia, Nuno,

Pedro and Rodolfo.

Lastly, I would like to thank the most important people in my life, my parents. Without them,

nothing would be possible, and I am grateful for all they have done for me. Thank you for all

the love and courage you gave me!


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Resumo

O Fabrico Aditivo (FA) descreve os processos que criam peças em 3D, sendo estas fabricadas

camada-por-camada. A tecnologia do FA já abrange, hoje em dia, uma grande variedade de

materiais, não havendo essa barreira quando é proposto um projeto. Permite também a

produção de mais peças em menos tempo, o que faz com que haja uma redução de custos e de

desperdício de material. A Otimização Topológica combina o método dos elementos finitos com

fórmulas matemáticas de otimização, proporcionando assim uma melhor distribuição de

material no domínio de referência da geometria em análise. Esta otimização pode ser aplicada

de modo a melhorar o desempenho de produtos já existentes ou para criar novos. Ao juntar

estas duas ferramentas, o FA com a otimização topológica, é possível criar estruturas mais

leves, com maior rigidez e complexidade. O que antigamente não era fazível, devido à limitação

nos moldes e ferramentas nos métodos tradicionais.

Esta dissertação procura a possibilidade de usar a otimização topológica como ferramenta para

obter uma asa, para um avião não tripulado (UAV), mais leve. O objetivo é investigar as

características de rigidez e resistência de uma asa, sendo apresentados diferentes casos para

análise. O trabalho descreve os designs e os procedimentos numéricos, em que se enquadram

a dinâmica dos fluidos computacional, as análises estruturais e a otimização topológica. A

otimização foi realizada com o objetivo de minimizar a massa. Todo o procedimento numérico

foi efetuado no software ANSYS.

Ao realizar este trabalho, houve um caso de estudo que se destacou apresentando uma redução

de 74% da massa, ainda assim para os requerimentos da aeronave em questão são necessários

mais estudos.

Palavras-chave

Asa, Fabrico Aditivo, Otimização Topológica


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Abstract

Additive Manufacturing (AM) describes the processes which produce 3D parts, being these

manufactured through a layer-by-layer procedure. The AM technology takes a wide variety of

materials, so there is not a barrier in that field when a project is proposed. It also allows the

part production in less time, reducing the costs and material waste. Topology Optimization

combines the finite element method with mathematical optimization formulas, providing a

better material distribution in the reference domain of the geometry under analysis. This

optimization can be applied to improve the performance of existing products or to create new

ones. By combining these two tools, AM and topology optimization, create lighter structures

with greater rigidity and complexity is possible. Which previously was not possible due to the

limitation in tools and molds of traditional methods.

This work searches the possibility of using topology optimization as a tool to obtain a lighter

wing to an unmanned aerial vehicle (UAV). The objective is to investigate the stiffness and

strength characteristics of a wing, being presented in different cases for analysis. This

dissertation describes the designs and numerical procedures, in which are included computation

fluid dynamics, structural analysis, and topology optimization. The optimization was realized

with the aim of minimizing mass. The entire numerical procedure was performed in ANSYS

software.

In this work, there is a study case which was evidencing, due to the 74% of weight reduction,

but for the aircraft requirements in the study, more investigations are necessary, since the

final design wing has, approximately, 1.5kg and the UAV should have a mass of 5kg.

Keywords

Wing, Additive Manufacturing, Topology Optimization


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Content

Chapter 1 ........................................................................................................ 1

Introduction .................................................................................................. 1

1.1 Motivation ..................................................................................... 1

1.2 Objectives .................................................................................... 2

1.3 Dissertation Outline ......................................................................... 2

Chapter 2 ........................................................................................................ 3

Literature Review ........................................................................................... 3

2.1 Additive Manufacturing ............................................................................. 3

2.1.1 Definition ........................................................................................ 3

2.1.2 Processes ........................................................................................ 3

2.1.3 Advantages and Disadvantages............................................................... 5

2.2 Materials .............................................................................................. 6

2.2.1 Polymers ......................................................................................... 7

2.2.1.1 Polylactic Acid (PLA) ........................................................................ 7

2.3 Printing Cases of Unmanned Aerial Vehicles (UAVs) .......................................... 9

2.3.1 FDM printed Fixed Wing UAV – AMRC UAV ............................................... 10

2.3.2 RecordRotor ................................................................................... 10

2.3.3 SULSA UAV ..................................................................................... 10

2.3.4 World’s First Jet-Powered, 3D-Printed UAV ............................................. 11

2.3.5 EASYMAX 001 .................................................................................. 11

2.3.6 University of Manito7gba – Team Kinect12 .............................................. 12

2.3.7 Air Force Institute of Technology ......................................................... 13

2.4 Structural Optimization .......................................................................... 15

2.4.1 Finite Element Method ...................................................................... 15

2.4.2 Topology Optimization ...................................................................... 16

2.4.3 SIMP: Solid Isotropic Material with Penalization ........................................ 18

Chapter 3 ...................................................................................................... 21

Numerical Methods ....................................................................................... 21


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3.1 Software description .............................................................................. 21

3.1.1 ANSYS ........................................................................................... 21

3.1.1.1 Workbench .................................................................................. 21

3.1.1.2 Fluent ........................................................................................ 21

3.1.1.3 Mechanical .................................................................................. 22

3.1.1.4 SpaceClaim/DesignModeler .............................................................. 22

3.1.2 CATIA ........................................................................................... 22

3.1.3 XFLR5 ........................................................................................... 22

3.2 Numerical Setup ................................................................................... 22

3.2.1 Analysis setup ................................................................................. 23

3.2.2 Fluent .......................................................................................... 23

3.2.2.1 Mesh .......................................................................................... 24

3.2.2.2 Setup ......................................................................................... 26

3.2.3 Mechanical .................................................................................... 27

3.2.3.1 Engineering Data ........................................................................... 28

3.2.3.2 Static Analysis .............................................................................. 28

3.2.3.2.1 Stress and strain formulas for an isotropic material .............................. 28

3.2.3.2.2 Stress and strain formulas for an orthotropic material ........................... 29

3.2.3.2.3 Setup ...................................................................................... 30

3.2.4 Topological Optimization ................................................................... 31

3.2.4.1 Analysis Settings ........................................................................... 31

3.2.4.2 Optimization Region ...................................................................... 32

3.2.4.3 Response Constraints ..................................................................... 32

3.2.4.4 Objective .................................................................................... 32

Chapter 4 ...................................................................................................... 35

Study Cases ................................................................................................ 35

4.1 Geometry ........................................................................................... 36

4.1.1 First Case ...................................................................................... 36

4.1.2 Second Case ................................................................................... 36

4.1.3 Third Case ..................................................................................... 37

4.2 Mechanical .......................................................................................... 37


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4.2.1 Mesh Element Quality ....................................................................... 37

4.2.2 Results .......................................................................................... 38

4.2.2.1 Equivalent Stress ........................................................................... 39

4.2.2.2 Total Deformation ......................................................................... 40

4.2.2.3 Percentage of Stress Error ............................................................... 41

4.3 Topology Optimization ........................................................................... 41

4.3.1 Optimization Region ......................................................................... 41

4.3.2 Results .......................................................................................... 42

4.4 Post-processing and design verification ....................................................... 45

4.4.1 Final design .................................................................................... 46

4.4.2 Structural Analysis ........................................................................... 47

Chapter 5 ...................................................................................................... 49

Conclusions and Future Work ........................................................................... 49

5.1 Conclusions ......................................................................................... 49

5.2 Challenges .......................................................................................... 49

5.3 Future Work ........................................................................................ 50

Bibliography ................................................................................................ 51

Appendixes ................................................................................................. 55

Appendix A .............................................................................................. 55

Appendix B .............................................................................................. 56

Appendix C .............................................................................................. 58

C.1 – First Case ....................................................................................... 58

C.2 – Second Case ................................................................................... 58

C.3 – Third Case ...................................................................................... 59

Appendix D .............................................................................................. 60


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List of Figures

Figure 1.1 – Generic process of CAD to part. ............................................................. 1

Figure 2.1 – Schematic of fused deposition molding (FDM) process. ................................. 4

Figure 2.2 – SULSA. .......................................................................................... 10

Figure 2.3 – Aurora Flight Sciences’ high-speed UAV is 80 percent 3D-printed with Stratasys’

additive manufacturing solutions. ........................................................................ 11

Figure 2.4 – EASYMAX 001. ................................................................................. 11

Figure 2.5 – View of one half of the wing assembly. .................................................. 12

Figure 2.6 – Carbon-fibre veneer adhered to frame module, making up the wing surface. .... 12

Figure 2.7 – Final geometry that was printed. .......................................................... 13

Figure 2.8 – Initial design space for TO, where blue corresponds to design space and red and

pink corresponds to non-design space, presented at left. Topology optimized is illustrated at

right. ........................................................................................................... 13

Figure 2.9 – 3D printed wing. .............................................................................. 14

Figure 2.10 – Timeline representing development of AM processes and UAV fabrications using

AM. ............................................................................................................. 14

Figure 2.11 – Three different structural optimization types. a) Size; b) Shape; c) Topology. . 15

Figure 2.12 – Example of a topological optimization. ................................................. 16

Figure 2.13 - SIMP flow chart. ............................................................................. 18

Figure 3.1 – Introduction to the overall procedure. ................................................... 23

Figure 3.2 – ANSYS Workbench. ........................................................................... 23

Figure 3.3 – Mesh around the aerofoil. ................................................................... 24

Figure 3.4 – Representation of element quality in ANSYS Fluent. .................................. 25

Figure 3.5a) – Domain boundaries definition, focus in symmetry and outlet. .................... 25

Figure 3.5b) – Domain boundaries definition, focus in symmetry and inlet. ...................... 25

Figure 3.6 – Axis system illustration. ..................................................................... 27

Figure 3.7 – Representation of the effect of the density filter on an arbitrary design variable

distribution.................................................................................................... 33

Figure 3.8 – Influence of filter factor b on the optimal layout. The ground structure consists of

120x40=4800 4-node elements and the volume is restricted to 50% of the design domain. ... 34


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Figure 4.1 – Image of the aerofoil obtained in XFLR5. ................................................ 35

Figure 4.2 – Illustration of the wing root. ............................................................... 36



Figure 4.6 – Representation of the element quality, for the first case. ........................... 37

Figure 4.7 – 10-noded tetrahedron element. ........................................................... 38

Figure 4.8 – Distribution of equivalent (von-Mises) stress over the wing, in Pa, where: a) first

case, b) second case and c) third case. ................................................................. 39

Figure 4.9 – Distribution of deformation over the wing, in m, where: a) first case, b) second

case and c) third case. ...................................................................................... 40

Figure 4.10 – Percentage of stress error, where: a) first case, b) second case and c) third case.

.................................................................................................................. 41

Figure 4.11 – Representation of exclusion and design regions, for the first case. ............... 42

Figure 4.12 – Representation of exclusion and design regions, for the second case. ........... 42

Figure 4.13 – Representation of exclusion and design regions, for the third case. .............. 42

Figure 4.14 – Representation of the removed material, of the first case. ........................ 43

Figure 4.15 – Representation of the retained region, of the first case. ........................... 43

Figure 4.16 – Representation of the removed material, of the second case. ..................... 43

Figure 4.17 – Representation of the retained region, where the tip of the wing is detached, of

the second case. ............................................................................................. 43

Figure 4.18 – Representation of the removed material, of the third case. ....................... 44

Figure 4.19 – Representation of the retained material, of the third case. The image focus on

wing’ tip to the interior. ................................................................................... 44

Figure 4.20 – Representation of the final geometry, as viewed from the side, in CATIA. ...... 46

Figure 4.21 – Representation of the optimized geometry, from the top, in CATIA. ............. 46

Figure 4.22 – Representation of the support from the connection between wing-fuselage. ... 47

Figure 4.23 - Distribution of equivalent (von-Mises) stress over the wing, in Pa. ................ 47

Figure C.1 – Objective convergence vs objective convergence criterion. ......................... 58

Figure C.2 – At left is presented the variation of global stress response and at right is the

variation of displacement response. ..................................................................... 58


Figure C.4 – At left is presented the variation of global stress response and at right is the

variation of displacement response. ..................................................................... 58


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Figure D.1 – Dimensions from the support geometry of the connection between wing-fuselage.

.................................................................................................................. 60


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List of Tables

Table 2.1 – Material properties of bulk PLA. .............................................................. 7

Table 2.2 – Ultimate tensile strength (MPa) of different thermoplastics 3D-printed by FDM. ... 8

Table 2.3 – Classification of UAVs as defined by UVS International. ................................. 9

Table 2.4 – Name of UAVs or printed parts for each type of AM technique. ........................ 9

Table 2.5 – Methods used for large ISE or IS topologies in generalized shape optimization. ... 17

Table 3.1 – Orthogonal Quality mesh metrics spectrum. ............................................. 24

Table 3.2 – Correspondence of percent of the number of elements with the classification of

orthogonal quality, a mesh metric from ANSYS Fluent. .............................................. 25

Table 3.3 – Properties of unidirectional carbon fibre reinforced plastics and PLA. ............. 28

Table 3.4 – Values of C for each type of element. ..................................................... 30

Table 4.1 – Aircraft’s data on Air Cargo Challenge 2017. ............................................. 35

Table 4.2 – Results from the mesh analysis used on different geometries. ....................... 38

Table 4.3 – Results from Mechanical analysis. .......................................................... 39

Table 4.4 – Results of the Topology Optimization, to the different study cases. ................ 42

Table 4.5 – Results of the final design, obtained in ANSYS. .......................................... 47

Table A.1 – Results from XFLR5, to a fixed speed of 24 m/s. ........................................ 55

Table B.1 – Aerofoil coordinates. ......................................................................... 56


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Nomenclature

b Filter factor [-]

B Bulk modulus [Pa]

C Constant [-]

C1ε Constant [-]

C2ε Constant [-]

Cµ Constant [-]

CL Lift coefficient [-]

Cm Constitutive matrix [Pa]

E Elastic Modulus [Pa]

E0 Elastic matrix of initial solid element [Pa]

Ei Elastic matrix [Pa]

F External force vector [N]

G Shear Modulus [Pa]

h Volume ratio [-]

H Sensitivity filter [-]

k Turbulent kinetic energy [m2/s2]

K Global stiffness matrix [Pa]

L Lift [N]

Lal Adjoint load vector [N]

N Total number of discrete numbers [-]

p Penalization [-]

rfilter Mesh filter radius [m]

S Wing area [m2]

Sut Ultimate tensile strength [Pa]

u Displacement vector [m]

U Global displacement vector [m]

X Design variable vector [-]

�̅�𝑖 Element volume after optimization [m3]

V Velocity [m/s]

V0 Initial volume [m3]

Vad Adjoint displacement vector [m]

wj Weight function [kg]

xi Position of element i [m]

xj Position of element j [m]

xt Ultimate longitudinal tensile strength [MPa]

yt Ultimate transverse tensile strength [MPa]


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Greek symbols

ε Strain [-]

εd Dissipation rate [m2/s2]

σ Stress [Pa]

σε Constant (Turbulent Prandtl number for dissipation

rate) [-]

σk Constant (Turbulent Prandtl number for kinetic

energy) [-]

σy Yield Strength [Pa]

σlim Yield stress limit [Pa]

σvm Von Mises stress [Pa]

ρ Density [kg/m3]

ρi Element i density [kg/m3]

𝜌�̃� Filtered i density [kg/m3]

ρj Element j density [kg/m3]

ρmin Minimum limit of element relative density [kg/m3]

µ Dynamic Viscosity [kg/(m.s)]

𝑣 Poisson’s ration [-]

Ω Reference domain [m3]


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Acronyms

3D Three Dimensional

ABS Acrylonitrile Butadiene Styrene

AM Additive Manufacturing

ANSYS Analysis of Systems

BC Boundary Condition

CAD Computer-Aided Design

FDM Fused Deposition Modelling

FEA Finite Element Analysis

FEM Finite Element Method

FGM Functionally Graded Materials

PLA Polylactic Acid

SIMP Solid Isotropic Material with Penalization

TO Topology Optimization

UAV Unmanned Aerial Vehicle

UBI Universidade da Beira Interior


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Chapter 1

Introduction

1.1 Motivation

Nowadays, parts are possible to manufacture through Additive Manufacturing (AM) technology,

more specifically 3D printing, which consists of a print of a three-dimensional model generated

using a CAD system, created by successive layers of material [1]. The original name for 3D

printing was rapid prototyping because a product could be rapidly and automatically created

without any complexity [2]. The term AM was given by the committee (F42) of American Society

for Testing and Materials (ASTM), in 2009 [2]. Since then, multiple new technologies using

different materials, including metallic, ceramic and polymeric materials, became commercially

available [3]. AM technology has been studied due to its advantages because it can be used to

remove or simplify many of multi-stage processes, reducing time when compared to traditional

methods. AM process is illustrated in Figure 1.1.

Figure 1.1 – Generic process of CAD to part [4].

AM can be combined with Topology Optimization (TO), which is a numerical method that

enables the weight optimization of any geometry complying with previously requirements.

These new methods and technologies allow the reduction of using parts that leads to fewer

critical failures. Considering these implications, safer aircrafts could be produced, and many

lives could be saved. Thus, the need to continue the development of these tools is crucial.


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1.2 Objectives

The purpose of this dissertation is to investigate the possibility of using TO in the design of a

small unmanned aerial vehicle (UAV) wing that is to be produced by an additive manufacturing

technology. For that, the following tasks were defined:

• Design geometry in CATIA V5 for implementation on CFD analysis;

• Structural analysis in ANSYS for different design geometries, applying the boundaries

conditions and the results from CFD analysis;

• Topology optimization of previous designs, with the intention of weight reduction.

1.3 Dissertation Outline

This dissertation is divided into 5 chapters. The first and current chapter includes motivation

and objectives.

The second chapter is dedicated to the literature review, where the technologies of AM are

presented, as well as, the advantages and disadvantages, including the materials used. Some

printing cases of UAVs and parts of its are also presented. TO is presented at the end of this

chapter, emphasizing the Solid Isotropic Material with Penalization (SIMP) method, where the

formulas behind the method are shown.

The numerical methods are described in the third chapter. Firstly, the software used is

described. Then, the numerical setup is presented, where it is divided into 4 sub-sections. The

first sub-section is a brief presentation of ANSYS Workbench. The second is dedicated to Fluent,

where the used model, mesh and boundary conditions (BCs) are being described. The third

includes the mechanical study, where the material’s properties are presented, and an

explanation of the setup. The fourth is dedicated to topology optimization.

The fourth chapter refers to the study cases and the results from mechanical and topology

optimization.

The fifth and final chapter reports the conclusions and possible future works for this topic.


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Chapter 2

Literature Review

2.1 Additive Manufacturing

2.1.1 Definition

In 2012, ASTM defined AM technology as capable of “joining materials to make objects from 3D

model data” [1]. The initial purpose of the technology was to create prototypes, for all sectors,

in a flexible and fast manner [2].

AM involves processes based on continuous deposition of material, layer-by-layer until a

physical object is created without labor resources, following instructions from a computer with

a virtual model designed in a CAD system. In these processes, metal, polymers, or ceramics

materials are used, through highly specialized machines [2]. For each of these technologies,

there are at least two materials: the production material and the support material. The support

is, in most of the cases, cleaned and becomes a manufacturing residue [5]. With the evolution

of materials and processes, AM became a natural tool to solve some specific problems for small

series direct production (rapid manufacturing), tooling production and more recently a

powerful tool to produce cost-effectively complex parts. Nowadays, faster and cheaper AM

techniques have been developed with high print quality. Polymer materials for 3D printing are

being produced with a wider range of properties [6].

These technologies are revolutionizing the world of manufacturing, bringing forward the so-

called Fourth Industrial Revolution (4.0 Industry), where the production processes tend to

become increasingly efficient, autonomous and customizable [3].

2.1.2 Processes

The commercial AM most used are:

1. Stereolithography (SLA)

SLA was the first commercially available process in 1986. Initially, there were only a few

materials that could be used, however, with today advancements, there is a greater variety.


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The basic concept of stereolithography is photocurable resin printing, typically acrylic or epoxy,

by exposing it to ultraviolet (UV) light of a specific wavelength, and then the exposed 2D-

patterned resin layers become solid through a process called photopolymerization [1, 2, 6].

2. Fused Deposition Modelling (FDM)

It is one of the most used techniques which uses a spool of a thermoplastic filament with varying

diameters to be melted and extruded through a heated nozzle. The materials used are nylon,

Acrylonitrile Butadiene Styrene (ABS), Polylactic Acid (PLA) and aerospace grade UltemTM. This

technique is based on automatic deposition of filament material and a filament of support one.

T5his process is repeated layer-by-layer, until the physical model is finished, as illustrated in

Figure 2.1. In the end, the support material is taken out through a process like ultra-sound

bath. Recently, thermoplastics with higher melting temperatures such as PEEK can already be

used as materials for desktop 3D printing, which are the most popular consumer-level polymer

composites 3D printers.

As long as the errors are below the accuracy level of the machine process (≈ 0.5mm), they are

acceptable. The machine’s language is STL and then it prints one layer (2D) on top of the other,

forming at the end a 3D object [2, 6, 7, 8].

Figure 2.1 – Schematic of fused deposition molding (FDM) process [8].

3. Selective Laser Sintering (SLS)

It is a process where a laser beam transfers energy into a surface containing a thin layer of pre-

heated powder material. The energy transferred by the laser beam fuses specific areas of the

surface. After fusing one layer, another one is deposited and again the laser fuses this layer

that will bind in the previous one [2].


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4. Multi Jet Modelling (MJM) or Polyjet

It is a process where a print head containing hundreds of nozzles selectively spreads in a surface

a photopolymeric material that is cured by the incidence of a specific wavelength. Another

print head spreads support material, normally in form of a gel that is also polymerized. It is a

continuous process where the platform is reduced to a tenth of a millimetre for each layer. In

the end, the support material is removed through a water jet [2].

5. 3D Printing (3DP)

It was developed by the Massachusetts Institute of Technology (MIT) and, today is one of the

most popular because of the low costs of acquisition and operation. It is a type similar to SLS

where a multi-nozzle print head selectively spreads a liquid binder in a platform with a powder.

The binder reacts with the powder to compose a layer while the platform is moved down. The

process repeats until the end of the part. The quality of the final product depends on powder

particle size, the viscosity of the binder, binder-powder interaction, and the speed of the

binder deposition [2, 6].

2.1.3 Advantages and Disadvantages

Advantages:

• Energy optimization: According to the USA Energy Department, AM can reduce energy costs

by 50% and material costs by 90%. The design and fabrication processes have been reduced

from weeks to a few hours [2, 6].

• Reduction in material waste: It is supposed that with AM, the only material required is the

one used to create parts. However, it is not completely true because sacrifice support

structures sometimes are necessary and some materials, special polymers, degrades with

continuous use under heating [2].

• Special tooling and speed: There is great flexibility to produce many different parts at the

same time, without the necessity of special tooling or equipment. AM systems are capable

to manufacture 3D components and products directly from raw materials and 3D design

data [1, 2].

• Design optimization: It is possible to produce complex shapes, so our mind is the limitation

[1, 6].

• Possibility to create low quantities of products, or just one, providing the absence of cost

relating to tools, as well as, reducing the number of parts in inventory since could be

produced on-site [1].

• Producing parts neglecting the prototype development phase. A direct translation of design

to component [3, 7].

• Different size ranges could be printed, from micro to several meters sized parts [2].


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Disadvantages:

• Slow process speed [1].

• Poor dimensional accuracy compared to some conventional processes [1].

• Rough surface finish and problems with process repeatability [1].

• The inherent anisotropic property of the printed parts. A result of AM techniques is that

the microstructure of the materials would tend to grow in a certain direction causing

different mechanical property along the layer. Consequently, parts manufactured through

additive processes show a preferential bearing direction, normally the one along which the

material is deposited [8, 9].

• AM is more economical when total build volume is lesser than 130 units, below that

injection moulding should be used. Additional processes are needed to make the material

into the forms that are suitable for AM processes, that is why material costs are higher than

conventional techniques [8].

2.2 Materials

The materials types used in AM processes have a large range, including metallic, ceramic and

polymeric materials along with combinations in the form of composites, hybrid or functionally

graded materials (FGM) [3]. Each process (mentioned in 2.1.2) requires different materials [8].

Mechanical properties of AM parts can be affected by unprinted materials and the technique

used. Nowadays, there are no standard tests for mechanical characterization because of the

undefined mechanical behaviour of 3D printed parts, and this happens for two reasons. Firstly,

because of the high number of parameters to control during the process. Secondly because of

the high anisotropy, which is defined by their manufacturing history, as the resistance of the

raw material and the cohesive forces between bonded layers [6]. Dizon et al. (2017) [6]

concluded that 3D-printed materials have large anisotropy, especially for the FDM and SLS

printed parts. The AM aim is to print a part with excellent quality with minimal anisotropy.

Between these materials, polymers have been mostly used perhaps due to their widespread use

in the first-generation rapid prototyping machines [3]. Polymers have relatively lower melting

and glass transition temperatures, which make it easier to flow at a relatively lower

temperature than ceramics and metals. Bonding involving metals and ceramics are not easy to

achieve, as it is with polymers due to their high melting temperatures. Normally, plastics have

lower strength than metals, however, they have lower density and higher strains at failure.

There are some cases that plastics will have higher strength, per unit weight, than metals [10].

In many cases are added special fillers as carbon nanotubes, graphene, nanocellulose, nanoclay

or nano silica to improve polymers performance [3], just like it happens with the project of

Zhang et al. [8]. They print the frame, tail, and gears for flapping wing UAV using ABS

copolymers material, after all, they found that using only ABS was not sufficient to provide the


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required strength, and then they reinforced the parts with carbon fibre rods and polyester films

for better strength.

Relatively to the characterization of powder materials and final products, Caputo et al. [11]

made a study. Since the processes of AM involve heat exchange phenomena, must be taken into

account the knowledge of the thermal behaviour of starting powder materials. Another

important aspect is their density and porosity. Porosity is a property that strongly affects the

quality of parts and for the measure of this feature there are ultrasonic non-destructive testing,

Archimedes method or micro X-ray computed tomography. Advanced image processing

techniques are useful in the AM environment to develop better quality control and reliability.

Non-destructive characterization methodologies allow to detect failures and to describe the

structure. They concluded that measuring the properties of powders is mandatory for the

industry to select proper raw materials.

2.2.1 Polymers

Polymers are macromolecules formed through smaller structural unities. They have structures

much more complex than metals or ceramics parts and they can be easily processed.

Nevertheless, they have low relative strength, elasticity module and operating temperature

limits.

Polymers are subdivided into two classes: thermoplastics and thermosetting. A thermoset is a

material that cures into a given shape, generally through the application of heat (curing is an

irreversible chemical reaction in which permanent connections are made between the

material’s molecular chains). A thermoplastic is a polymer that shapes with the application of

heat,i.e. its viscosity becomes smaller on heating. Cooling to room temperature makes the

strongest thermoplastics [10].

2.2.1.1 Polylactic Acid (PLA)

The most frequent source materials for commercially-available FDM printers are ABS and PLA.

Bulk PLA characteristics can be seen in Table 2.1.

Table 2.1 – Material properties of bulk PLA [12].

Material property Units Value

Density (ρ) kg/m3 1240 Elastic modulus (E) Pa 3500×106 Shear modulus (G) Pa 1287×106 Poisson’s ratio (v) - 0.36 Yield strength (σy) Pa 70×106

Ultimate tensile strength (Sut) Pa 73×106 Elongation % ~7


8

Industrial and general use of PLA is increasing due to the fact of its biocompatibility with the

environment, and for this reason, now many desktop consumer printer models use, exclusively,

PLA.

Torres et al. (2015) [12] present a study where they tested torsion of PLA materials resulting

from FDM and the effects of processing parameters including layer thickness, percent infill, and

post-processing via heat treatment. They concluded that heat treatment can cause an increase

in strength, especially in low-infill components. But this increase in strength provides a loss in

ductility.

Some studies have recently reported the tensile strength of different polymers, as summarized

in Table 2.2.

Table 2.2 – Ultimate tensile strength (MPa) of different thermoplastics 3D-printed by FDM [13].

Raster Angle ABS Polypropylene Polycarbonate PLA PEI

90º 26 32 19 54 40 0º 34 36 59.7 58 59

Authors Rezayat et al. Carneiro et al. Hill et at. Letcher et al. Bagsik et al.

These studies revealed that PLA has a better mechanical response than the other thermoplastics

polymers, and in tensile strength plane these materials are anisotropic, with the strength along

the direction of extrusion (0º) exceeding that in the transverse direction (90º). Research by Ahn

et al. [13] showed that the printing orientation and air gap had the most significant impact on

the mechanical properties of the printed objects; but on the other side, the printing orientation

and the platform temperature have a significant impact on structural inhomogeneity.

Y. Song et al. (2017) [13] quantify anisotropy and asymmetry of the mechanical response of PLA

parts produced by FDM. The elastic material response was transversely isotropic for 3D-printed

specimens and isotropic for injection-moulded specimens. They study specimens of porosity of

order 1% and conclude that the porosity of 3D-printed material can be minimised by optimising

the temperature and speed of extrusion, as well as, the speed of the printing head.

Manufacturing by 3D-printing increases the crystallinity of the material, reducing its ductility

and increasing the fracture toughness. The elastic response of 3D-printed material is

transversely isotropic, although the anisotropy is smooth. They proved that 3D-printing does

not affect material elasticity because both axial and transverse stiffness are similar to the one

in injection-moulded PLA and the inelastic response of the material is ductile and orthotropic.

They conclude that 3D printed PLA is tougher than injection-moulded PLA, due to the layered

and filamentous nature of 3D-printed material and the complexity that this induces in the

microscopic mechanisms of fracture. These experiments showed that in compression the

material stiffness was nearly independent of axial strain, indicating a response governed solely

by plasticity, with negligible damage. In contrast, in tension the material stiffness decreased


9

as a function of strain, indicating the presence of damage mechanisms in conjunction with

material’s plasticity.

2.3 Printing Cases of Unmanned Aerial Vehicles (UAVs)

Unmanned aerial vehicles are gaining popularity due to their application in military, private

and public sector, especially where human operator is not required. Evolution of UAVs started

during World War II and it has come a long way for all operations, military and non-military.

Birds and insects are the inspiration for some UAV’s designs and the most desired are the light-

weight UAVs due to a better performance in terms of shorter take-off range and longer flight

endurance. When operating at low Reynolds number the performance largely depends upon a

complex combination of specific and precisely orientated geometrical forms, for example,

flapping wing UAV has several potential benefits over fixed wings, as a better manoeuvring,

low speed, landing, and vertical take-off. Although a UAV design is specific to its mission

requirements, having high endurance is something that all have in common [8]. Table 2.3

summarizes the classification of UAVs as defined by UVS International.

Table 2.3 – Classification of UAVs as defined by UVS International [8].

UAV category Range [km] Flight altitude

[m] Endurance [hours]

Max. take-off weight [kg]

Micro <10 250 1 <5 Mini <10 150-300 <2 <30

Medium range 70-200 5000 6-10 1250 Medium altitude long

endurance >500 14000 24-48 1500

High altitude long endurance

>2000 20000 24-48 12000

Recent research on cellular structures and topology optimization have resulted in complex

light-weight UAV structures that cannot be fabricated using conventional manufacturing

techniques, so AM presents itself as a better option because there is no design limit [8]. Table

2.4 shows which AM technology was used for a UAV component or even an entire UAV.

Table 2.4 – Name of UAVs or printed parts for each type of AM technique [8].

Types of AM techniques Name of UAVs/ printed parts

FDM Fully printed; AMRC UAV; VAST UAV; Frame, gear, tail

Polyjet Lattice structure; Wing strut; Ornithopter; Replica of insect wing

SLA Entomopter; Stingray UAV; Flap; Wind tunnel; UAV model

SLS SULSA UAV; Scaled-down UAV; tunnel test; Spotter UAV


10

2.3.1 FDM printed Fixed Wing UAV – AMRC UAV

During the built process of FDM is necessary a broad number of support material in order to

prevent deformation, and this adds a direct material cost and significantly increases built time.

In 2014, a prototype UAV was design, manufacture and flight test by a team of engineers from

AMRC’s (Advanced Manufacturing Research Centre) new Design & Prototyping Group (DPG),

entirely of ABS plastic (ABS-M30), using FDM technology. For printing large components, such

the airframe, FDM was chosen, took less than 24 hours, which would be unthinkable because

before of AM optimization, the airframe would take 120 hours to produce. The UAV showed

good stability, and low aerodynamic noise at speed indicated an efficient wing design [14].

2.3.2 RecordRotor

In 2015, Altair Engineering in cooperation with Politecnico di Torino developed components for

a structure of a multi-rotor, named RecordRotor. The challenge was to interface arms,

consisting of carbon fibre tubes, with motor or frame, in 7075 Alloy. They use topology

optimization to minimize the weight and additive manufactured polymer components played

an important role in the prototype which was designed at the upper boundary of the normative

with an MTOW of 25kg. They demonstrate that with a scientific methodology and with the

support of innovative design tools was possible to construct high-performance components for

the aerospace industry, with optimization included [7].

2.3.3 SULSA UAV

Figure 2.2 – SULSA [15].

SULSA (Southampton University Laser Sintered Aircraft) was the first ‘printed’ aircraft.

Professors Andy Keane and Jim Scanlan from the University’s Computational Engineering and

Design Research group led the project. Kean’s team set out how quickly they could design a

1.5-metre wingspan, super-low-drag UAV, print it and get it airborne. The plane parts took two

days to design and five days to print, making this UAV a one-week plane. The constraints in the


11

project were that they needed the use of a launch catapult and a belly landing because there

was no undercarriage to keep complexity and weight down [15, 16].

2.3.4 World’s First Jet-Powered, 3D-Printed UAV

Aurora Flight Science and Stratasys Ltd developed a 3D-printed, jet-powered UAV with the

ability to reach speeds up to 241 km/h. It has a wingspan of 3m and weighs only 15kg, as

illustrated in Figure 2.3. 80% of the UAV was created using FDM process and the fuselage was

made of nylon and the engine exhaust duct was 3D-printed in metal [17].

Figure 2.3 – Aurora Flight Sciences’ high-speed UAV is 80 percent 3D-printed with Stratasys’ additive manufacturing solutions [17].

2.3.5 EASYMAX 001

EASYMAX 001 has a wingspan of 1527mm, as presented in Figure 2.4. It is easily printed and

possible to buy it, with a cost of 20$ and with an instruction manual included. Even the wing

and the fuselage have a 3D structure reinforcement, which makes the UAV very rigid while

maintaining a lightweight, even when it is made only from polymers [18].

Figure 2.4 – EASYMAX 001 [18].


12

2.3.6 University of Manito7gba – Team Kinect12

In 2011, the Composites Innovation Centre (CIC) requested Team Kinect12, from the University

of Manitoba, to develop a manufacturing process for a small airplane wing, which utilizes rapid

prototyping. The objectives that the client established was that the wing should weight no

more than 0.45kg and must structurally be capable of lift and support a 2.3kg UAV. The process

should also avoid the traditional methods of UAV wing construction and should be applicable to

other structures.

The final wing design, of Team Kinect12, consists of RP frame modules, carbon fibre veneers,

webs, and a spar. The veneers are adhered to the exterior shell to provide torsional strength

for the wing and additionally provide the surface of the aerofoil, as represented in Figure 2.5

and Figure 2.6. The spar is to provide high specific strength and covers the entire span of the

wing at 25% of the chord. The frame is produced in nine different modules, printed in ABS [19].

Figure 2.7 illustrates the final geometry that was printed through rapid prototyping.

Figure 2.5 – View of one half of the wing assembly [19].

Figure 2.6 – Carbon-fibre veneer adhered to frame module, making up the wing surface [19].


13

Figure 2.8 – Initial design space for TO, where blue corresponds to design space and red and pink corresponds to non-design space, presented at left. Topology optimized is illustrated at right [20].

Figure 2.7 – Final geometry that was printed [19].

The team’s setback was that RP machine had a lower resolution than some of the details

provided in CAD models, so these details were not printed, and thus were not included in final

geometry. But still, they were able to accomplish all the requirements established by CIC.

2.3.7 Air Force Institute of Technology

Walker et al. (2015) [20] decided to join AM with TO with the objective of creating a complex

wing structure. The TO objective was minimizing compliance, which means maximizing the

stiffness. They decided to apply the optimized wing in a UAV due to the relaxed airworthiness

requirements. The final objective of their work was focused only on the main wing body

structure, disregarding internal components like fuel tank, electronics, and cables. The wing

structure had two small structural constraints near the centre of the design space. All the

analysis was conducted considering only the skin of the wing, spars, and ribs. The wing was

structurally constrained at the wing root and aerodynamic forces were applied for defined

conditions.

For TO, the wing skin was considered a non-design space. The design space, the region where

the optimization occurred, was the wing interior. And in the centre of design space, there were

two small structural constraints, which belongs to non-design space (the region where

optimization does not occur). The optimization constraint used was to maintain a volume

fraction of the overall design space of less than 30 percent and the material used by them was

an aluminum alloy. Figure 2.8 shows the initial design after the optimization and shows the

structure after TO.


14

Fig

ure

2.1

0 –

Tim

eline r

epre

senti

ng d

evelo

pm

ent

of

AM

pro

cess

es

and U

AV f

abri

cati

ons

usi

ng A

M [

8].

Figure 2.9 presented the 3D printed wing, which was the purpose of the work.

Figure 2.9 – 3D printed wing [20].

Figure 2.10 is representing the timeline of the evolution of AM’s processes and development of

UAVs.


15

2.4 Structural Optimization

A continuum structure, relatively to the structural optimization, can be divided into Shape

Optimization, Size Optimization and TO, as illustrated in Figure 2.11. Compared to the first two

optimizations, TO can change the structure of the part, achieving designs that are not greatly

constrained by the nature of the initial design [21, 22]. TO matches Finite Element Method

(FEM) with mathematical formulas of optimization, with the aim of providing the best material

distribution [23].

Figure 2.11 – Three different structural optimization types. a) Size; b) Shape; c) Topology [24].

2.4.1 Finite Element Method

The FEM is a mathematical approach in which to solve a problem it subdivides into smaller

elements that keep the same properties compared to the initial. Differential equations are used

to describe these elements and are solved by mathematical models to obtain results with more

accuracy, but only gives an approximate solution [25, 26]. Several Finite Element (FE) based

methods have been developed for topology optimization of continuum structures. The Finite

Element Analysis (FEA) method, originally introduced by Turner et al. (1956) [27], is a powerful

computational technique for approximate solutions to a variety engineering problems, having

complex domains subjected to general BCs. It has become an essential step in the design or

modelling of a physical phenomenon. This physical phenomenon occurs in a continuum domain

involving several variables and the field of variables vary from element point to point,

possessing an infinite number of solutions in the domain. FEA reduces the problem to a finite

number dividing the domain into elements and expressing the unknown field variable in terms

of the assumed approximating functions within each element. These functions are defined by

the nodes, and these nodes are usually located along the element boundaries, and they connect

adjacent elements [28, 29].


16

2.4.2 Topology Optimization

The coupling between AM and TO provides innovations forms, which with traditional

manufacturing could be impossible to turn them into a part, but with additive manufacturing

it is conceivable, and it can be applied in plastics, metals, etc. [5]. Over the last decade, TO

has appeared as one of the numerous optimization techniques being used by most aircraft

manufacturers due to its capability to generate light-weight conceptual designs [30]. The

purpose of this optimization is to find the optimal layout within a specified region, knowing the

support conditions, the applied loads and the volume constraints, being unknown the shape,

the physical size and the connectivity of the structure [31]. TO has important practical

applications by the manufacturing (i.e. car and aerospace) industries and has a significant role

in micro and nanotechnologies [28].

In 1977, Prager and Rozvany [28] formulated the first general theory of topology optimization.

Many optimization methods such as homogenization technique (Bendsøe and Kikuchi 1988 [28]),

solid isotropic material with penalization (SIMP) (Bendsøe 1989; Zhou and Rozvany 1991 [28])

and evolutionary structural optimization (ESO) (Xie and Steven 1993, 1997 [28]) have been

developed. SIMP, that was developed in the late eighties, and BESO is the most widely used

algorithms, owing to their efficiency and simplicity [22, 32]. BESO (bi-directional ESO) is the

latest version of ESO. It is a combination of additive evolutionary structural optimization (AESO)

and ESO. In this method, the wasteful material is removed while efficient material is added to

the structure, at the same time. However, BESO is limited to the TO of an objective function

such as mean compliance with a single constraint, as structural volume [28, 29, 33]. SIMP will

be discussed later in subchapter 2.4.3 since will be the method used in this dissertation.

As previously presented AM materials are constituted by production material and the support

one and this optimization can match both, as exemplified in Figure 2.12.

Figure 2.12 – Example of a topological optimization [5].


17

TO problem can be defined as the search for the best allocation or distribution of material in a

given design space. The reference domain Ω (Ω Є R3) is determined by the design space, loads

and BCs. The design space corresponds to the interior of the objects and a non-design space

corresponds to the skin of the object [5].

About existing topological optimization models, these can be divided according to the type of

topology involved. Taking in consideration that the first term corresponds to the base material

and the second to the type of elements, there are four large groups being designated as

Isotropic-Solid (IS), Isotropic-Solid/Empty (ISE), Anisotropic-Solid/Empty (ASE) and Isotropic-

Solid/Empty/Porous (ISEP) (includes Isotropic-Solid/Empty/Composite (ISEC) and Isotropic-

Solid/Empty/Composite-Porous (ISECP)) [30]. For simplicity, the ISE and IS topologies are

specified in this work. Within the models ISE and IS there are used the following strategies:

Solid Isotropic Microstructures with Penalization (SIMP), Optimal Microstructures with

Penalization (OMP), NonOptimal Microstructures (NOM) and Dual Discrete Programming (DDP).

Below explained the strategies in Table 2.5:

Table 2.5 – Methods used for large ISE or IS topologies in generalized shape optimization [32].

SIMP as becoming generally accepted in topology optimization as a technique of considerable

advantages.

SIMP OMP NOM DDP

Microstructure of elements

Solid, isotropic Optimal nonhomogeneous

Nonoptimal nonhomogeneous

Solid, isotropic

Additional penalization

Yes Yes No Not necessary

Homogenization necessary

No Yes Yes No

Number of free parameters

1 2D:3ou 4

3D:5 ou 6

>1 1

Available for: All combinations

of design constraints

Compliance All combinations of design constraints

Compliance

Penalization adequate

Yes Yes No -


18

2.4.3 SIMP: Solid Isotropic Material with Penalization

Figure 2.13 - SIMP flow chart [22].

The term “SIMP” is sometimes called “material interpolation”, “power law”, “artificial

material” or “density” method [28]. The basic idea of this method is discretizing the design

domain by finite element mesh and optimize the density variables associated to each element

within the discretization, as represented in Figure 2.13 [33]. The design variables are a series

of material densities, which are denoted by ρi Є [0,1]. Each node in the finite element mesh

has its own density variable, ρi, and the element shape functions are used to construct a

continuous density field. Regions where ρ≈ 0 are interpreted as being void of material, while

regions where ρ=1 are interpreted as being solid, because intermediate density values are just

a mathematical tool for representing non-physical stated, the SIMP formulation penalizes

intermediate densities using an exponential penalty function and the results will depend on the


19

degree of penalization [30]. The relationship of elastic matrix Ei, the effective Young’s

modulus, and element density ρi in optimization process can be written as

𝐸𝑖 = 𝜌𝑖𝑝𝐸0 (2.1)

where p is a penalization value and E0 elastic matrix of the initial solid element [34]. For p=1,

the problem corresponds to the classical ‘variable thickness sheet optimization’ which is

studied by Cheng and Olhoff and lots of grey density elements 0<ρi<1 which have no physical

meaning are obtained. Choosing p too low or too high either causes too much grey scales or too

fast convergence to local minima, and lots of numerical examples show that p=3 ensures good

convergence to almost 0-1 solutions [33].

SIMP is used in practice for highly complex non-convex problems and most commercial TO

software have implemented SIMP for TO, being ANSYS one of them [22, 28].


20


21

Chapter 3

Numerical Methods

3.1 Software description

Nowadays, technology allows the numerical study without experimental tests, giving the

opportunity to realize studies that in an experimental way have a high cost. In this chapter, it

will be discussed the software used, in a succinct way.

3.1.1 ANSYS

ANSYS is the original name for commercial products. The company develops a complete range

of CAE (Computer Aided Engineering) products. It is a general-purpose finite-element modelling

package for numerically solving a wide variety of mechanical problems. These problems include

static/dynamic, structural analysis (both linear and nonlinear), heat transfer, and fluid

problems, as well as acoustic and electromagnetic problems [35].

3.1.1.1 Workbench

ANSYS Workbench helps drive all of the simulations in a single environment. The platform guides

the user through complex multiphysics analyses with drag and drops simplicity, providing bi-

directional CAD connectivity [36]. ANSYS Workbench is often used in conjunction with CAD

software such as DesignModeler or SpaceClaim.

3.1.1.2 Fluent

ANSYS Fluent provides comprehensive modelling capabilities for a wide range of incompressible

and compressible, laminar and turbulent fluid flow problems. Steady-state and transient

problems can be performed. In this type of analyse a broad range of mathematical models for

transport phenomena is combined with the ability to model complex geometries. A very useful

group of models in Fluent is the set of free surface and multiphase flow models, therefore, can

be used for analysis of gas-liquid, gas-solid, liquid-solid and gas-liquid-solid flows. Accurate and

robust models are a vital component of Fluent suite of models [37].


22

3.1.1.3 Mechanical

Mechanical is a module in ANSYS to set up and run structural analyses. Topology optimization

was introduced in 2018 with ANSYS 18.0, integrating its own solver and pre and post-processing

tools [24].

3.1.1.4 SpaceClaim/DesignModeler

SpaceClaim and DesignModeler are CAD software integrated into several modules of ANSYS.

SpaceClaim is the most recent and more upset to topology optimization because it can read

STL files exported from Mechanical and post-process the geometry before design validation.

The geometry is converted then into a solid for ANSYS Mechanical to analyse again as validation

process.

3.1.2 CATIA

It is a multi-platform software suite for CAD, computer-aided manufacturing (CAM), CAE

developed by the French company Dassault Systèmes.

3.1.3 XFLR5

XFLR5 is an analysis tool for aerofoils, wings, and planes operating at low Reynolds Numbers.

3.2 Numerical Setup

In this chapter, the numerical methods and the numerical setup will be presented. Firstly,

ANSYS Workbench will be explained. The second section is dedicated to ANSYS Fluent,

describing the flow properties, that uses various convergence schemes to equate the flow

properties along the boundaries and the principal aim of this section is to calculate lift, drag

and pressure distribution along the wing. In this section mesh quality and model, setup is

described. The third section corresponds to the Mechanical part and material data is provided,

the mesh quality and the steps that have been taken in setup, in a general way, because there

is be given more emphasis of this part in the next chapter. The fourth section refers to the

topology optimization, including the design and exclusion regions, and the objective of the

problem. Figure 3.1 illustrates the overall procedure, for better comprehension.


23

Figure 3.1 – Introduction to the overall procedure.

3.2.1 Analysis setup

Figure 3.2 shows a typical setup in ANSYS Workbench. Firstly, an analysis is made in Fluent, in

order to determine the wing’s pressure distribution. Then, after the meshing is done in Static

Structural and the loads are applied, the topology optimization can be initiated with the results

from the two-previous analysis. The last analysis in Mechanical is to validate the design.

Figure 3.2 – ANSYS Workbench.

3.2.2 Fluent

Wing structures have a significant role because they are responsible to create lift. In movement,

pressure distribution around the aerodynamic surface is created, which translates into the

aerodynamic force. Fluent is used to determine the pressure distribution around the wing

surface, in this dissertation.


24

3.2.2.1 Mesh

Figure 3.3 – Mesh around the aerofoil.

Figure 3.3 shows the geometry mesh, giving more focus to the wing surface. The mesh is

obtained due to parameters that ANSYS provide, being generated automatically, and in this

case, have 102571 nodes and 562983 elements. For flow analysis, the mesh should be defined

between the aerofoil walls and the boundaries. These boundaries the further away from the

aerofoil, better, meanwhile for this type of analysis the ambient conditions are used to define

the BCs. In this study the boundaries are in a distance 20 times bigger than the aerofoil chord,

to make results more accurate.

In this Fluent’s section, it is possible to view the orthogonal quality, through mesh metric. This

parameter is to ascertain the mesh quality, providing a scale between 0 and 1, and the closer

to 1 the better the element. This metric is based on the following scale, as it is represented in

Table 3.1:

Table 3.1 – Orthogonal Quality mesh metrics spectrum [38].

Unacceptable Bad Acceptable Good Very good Excellent 0-0.001 0.001-0.14 0.15-0.20 0.20-0.69 0.70-0.95 0.95-1.00

Figure 3.4 and Table 3.2 show the number of elements within each quality range. Based on

Table 3.1, it is verified that 0.09% of the elements are below acceptable.


25

Figure 3.4 – Representation of element quality in ANSYS Fluent.

Table 3.2 – Correspondence of percent of the number of elements with the classification of orthogonal quality, a mesh metric from ANSYS Fluent.

Classification Percent of number of elements

Unacceptable 0% Bad 0.09%

Acceptable 0.004% Good 18.874%

Very Good 75.135% Excellent 5.897%

The BCs must be assigned to the faces of the control volume. In the present case, three types

of BCs are used: symmetry, inlet, and outlet. The symmetry condition is applied to the face

that contains the root of the wing because, since symmetric flight conditions are to be analysed,

only half of the wing needs to be simulated. The inlet conditions are applied to the face

upstream of the wing. The outlet conditions are applied to the face downstream of the wing,

the face upper and down. Figure 3.5a) and Figure 3.5b) exemplifies the faces where the BCs

are applied, where A corresponds to symmetry, B is the inlet and C, D, E and F the outlet.

Figure 3.5a) – Domain boundaries definition, focus in symmetry and outlet.

Figure 3.5b) – Domain boundaries definition, focus in symmetry and inlet.


26

3.2.2.2 Setup

The solver chosen was the pressure-based solver, since it is suitable in incompressible and

mildly compressible flows. The velocity formulation chosen was absolute because it is

preferable in applications where the flow in most of the domain is not rotating. The steady-

state simulation was chosen due to its easier convergence as there are fewer terms to model.

After computing solutions with different turbulent models such as, k-omega SST model and

transition k-kl-omega (3 eqn), the standard k-epsilon (ε) turbulent model is used since its results

presented are more similar to the ones that result from XFLR5, relatively to L and CL. This

model is commonly used, and it was developed by Jones and Launder and has been modified

by other investigators. It gained popularity in industrial flow owed to its economy, toughness,

and reasonable accuracy for a wide range of turbulence flows. K-ε model is based on model

transport equations for the turbulence kinetic energy (k) and its dissipation rate (εd), assuming

that the flow is fully turbulent, and the effects of molecular viscosity are negligible. C1ε, C2ε,

and Cµ are constants that have the following values: 1.44, 1.92 and 0.09, respectively. σk is the

turbulent Prandtl number for k, which has the value of 1.0 and σε is the turbulent Prandtl

number for ε, which is equal to 1.3. These values have been determined from experiments for

fundamental turbulent flows and they work well for a wide range of wall-bounded and free

shear flows.

The fluid used is air with the following properties: ρ=1.225kg/m3 and µ=1.7894×10-5kg/(m.s).

As mentioned in subsection 5.2.2.1, the BCs were applied on the faces. The inlet, referred to

as face B in Figure 3.6b), corresponds to the Velocity Inlet, and these data are in functions of

velocity, its magnitude, and direction. The direction of the velocity, in component y and z, was

based on the angle of attack to the most critical flight condition, which for this UAV was 11º,

according to the preliminary results obtained in XFLR5 for a Reynolds number of 3.94×105. The

results obtained in XFLR5 were based in an analysis, with speed fixed of 24m/s, based on the

method of horseshoe vortex (VLM1). As explained in section 3.1, XFLR5 is an analysis tool for

wings operating at low Reynolds numbers, and for this reason, this software was used, as a way

of comparison with the results obtained in Fluent. According to Table A.1, from the Appendix

A, for a maximum take-off weight of 150N, the angle of attack corresponding is, approximately,

11º, so, for this reason, the chosen angle was this, as it was previously said. The correspond CL

for this condition is 1.765. These parameters were obtained through the following lift formula:

𝐿 =1

2𝜌𝐶𝐿𝑉

2𝑆 (3.1)

where L represents lift, CL is the lift coefficient, V is the velocity of the aircraft, ρ is the air

density, which changes due to altitude, and S is the wing area. The lift must be equal to the

aircraft’s weight.


27

The output data was the Pressure Outlet (letter C, in Figure 3.6a)), which allows defining an

outlet pressure differential equal to zero, allowing the flow to develop freely and in it's entirely

within the control volume.

3.2.3 Mechanical

In general, a finite-element solution may be broken into three stages:

• Preprocessing - defining the problem: the key points, areas, lines, volumes, the

element type and material/geometrical properties and mesh.

• Solution – Assigning loads, constraints and solving.

• Postprocessing – further processing and viewing of the results [35].

In this section, the parameters that are evaluated corresponds to equivalent (von-Mises) stress,

total deformation, and strain energy. But for this evaluation, first, the materials to be used

throughout the work are characterized. Then, the mathematical formulas of the parameters

are established below, both for isotropic materials, in this work is PLA, and for orthotropic

materials, which is the case of fibre carbon.

To obtain an accurate result is necessary, then, to create a mesh in the structure, under study.

A mesh is composed of elements and nodes. The structure is divided by elements, and these

elements are connected by nodes. After the resulting mesh, it is necessary to apply the BCs, so

that the software does the static analysis.

For all the geometries analysed in Mechanical and TO, the axis system is the same. The x-axis,

where occurs the wingspan variation, has an interval from 0 to 1m, when x is equal to zero

corresponds to wing root and when x is equal to 1m corresponds to wing tip. The y-axis positive

describes the chord variation, and the interval varies between 0 to 0.25m. Finally, the z-axis

corresponds to the wing height. Figure 3.6 exemplify the axis system.

Figure 3.6 – Axis system illustration.


28

3.2.3.1 Engineering Data

Two materials are used in this work, polylactic acid (PLA) and unidirectional carbon fibre

reinforced plastic (CFRP). The properties of these materials are summarized in Table 3.3.

Table 3.3 – Properties of unidirectional carbon fibre reinforced plastics and PLA [39, 40].

Orthotropic Material Isotropic Material

UD-CFRP PLA

Density [kg/m3] 1600 Density [kg/m3] 1240 Ex [MPa] 121×103

E [MPa] 3500 Ey [MPa] 7.46×103 Ez [MPa] 7.46×103

νxy 0.31 v 0.36

νyz 0.44 νxz 0.31

G [MPa] 1.29×109 Gxy [MPa] 5.18×103 Gyz [MPa] 2.59×103

B [MPa] 4.17×109 Gxz [MPa] 5.18×103 xt [MPa] 1500

σ [MPa] 73 yt [MPa] 50

For isotropic materials, the data are introduced by the user, except the shear modulus and the

bulk modulus, which are computed from the following expressions, respectively [41]:

𝐺 =𝐸

2(1 + 𝑣) (3.2)

𝐵 =𝐸

3(1 − 2𝑣) (3.3)

where E is the elastic modulus and 𝑣 is the poisson ratio.

3.2.3.2 Static Analysis

A static structural analysis determines the displacements, stresses, strains, and forces in

structures. Firstly, the displacements are calculated through the following expression:

𝐾𝑈 = 𝐹 (3.4)

where K is the stiffness matrix of the structure, U is the displacement vector and F is the

external force vector applied to the structure. After displacement’s calculation, the strain and

the stress of the structure can be determined.

3.2.3.2.1 Stress and strain formulas for an isotropic material

The following expressions are relative to the strain (ε):


29

x-direction 𝜀𝑥 =1

𝐸[𝜎𝑥 − 𝜈(𝜎𝑦 + 𝜎𝑧)]

(3.5) y-direction 𝜀𝑦 =1

𝐸[𝜎𝑦 − 𝜈(𝜎𝑥 + 𝜎𝑧)]

z-direction 𝜀𝑧 =1

𝐸[𝜎𝑧 − 𝜈(𝜎𝑥 + 𝜎𝑦)]

where E is Young’s modulus and ν is the Poisson’s ratio of the material.

The stress is computed by Hooke’s law, as it is represented below:

𝜎 = 𝐶𝜀 (3.6)

In the case of a 3D element and for isotropic materials, Cm is the constitutive matrix given by:

[𝐶] =𝐸

(1+𝑣)(1−2𝑣)

−

−

−

−

−

−

2

21

02

21

002

21

0001

0001

0001

vSymmetry

v

v

v

vv

vvv

(3.7)

where E is the modulus of Young and v is the Poisson’s ratio of the material [42].

3.2.3.2.2 Stress and strain formulas for an orthotropic material

Fibre-reinforced composites contain, in general, three orthogonal planes of material property

symmetry and are classified as orthotropic materials.

The following equation gives the stress-strain relationship:

=

12

13

23

33

22

11

66

55

44

33

2322

131211

12

13

23

33

22

11

0

00

000

000

000

CSymmetry

C

C

C

CC

CCC

(3.8)

These equations can be inverted, introducing elastic constants E, ν and G:


30

−−

−−

−−

=

12

31

23

33

22

11

12

13

23

32

23

1

13

3

32

21

12

3

31

2

21

1

12

31

23

33

22

11

2

100000

02

10000

002

1000

0001

0001

0001

G

G

G

EE

v

E

v

E

v

EE

v

E

v

E

v

E

(3.9)

where Ei is Young’s modulus of the material in direction i=1,2,3; νij is the Poisson’s ration

representing the ratio of a transverse strain to the applied strain, for example, v12=-ε2/ε1, for

uniaxial tension in the direction 1 [43].

3.2.3.2.3 Setup

In this section, the procedures are discussed with respect to structural analyses, in a succinct

approach, while in Chapter 4 these procedures are applied to each study case, with the results

presented and discussion of its.

First, the material should be applied to the structure, which was defined in the last section.

Then, a mesh with tetrahedron elements is created. The quality of the mesh is assessed by a

mesh metric parameter which provides a value between 0 and 1 based on the geometry of the

elements. In this scale, a value closer to 0 indicates lower element quality and a value closer

to 1 indicates better element quality. This mesh metric used is “element quality” and it is

based on the following expression:

𝑄𝑢𝑎𝑙𝑖𝑡𝑦 = 𝐶 [𝑣𝑜𝑙𝑢𝑚𝑒/√[[(𝑒𝑑𝑔𝑒 𝑙𝑒𝑛𝑔𝑡ℎ2]3]] (3.10)

The following table lists the value of C for each type of element.

Table 3.4 – Values of C for each type of element.

Element C

Triangle 6.92820323

Quadrangle 4.0

Tetrahedron 124.70765802

Hexagon 41.56921938

Wedge 62.35382905

Pyramid 96


31

The criteria of quality mesh control is defined as 75% of the elements obtain a quality above of

75% and to prove the accuracy of the results is presented the percentage of stress error, in

Chapter 4.

After meshing, BCs needed to be applied. For all the analysis, the BCs are the same, which are

fixed support, on the faces where spars are intended. The fixed support has the objective of

restricting the six degrees of freedom, which are translations and rotations in x, y, and z-axis.

Pressure distribution is also applied around the wing surface. This last parameter comes from

ANSYS Fluent.

As TO is done after structural analysis, it is not possible to considerer, in this dissertation, the

large deflection, since ANSYS TO does not support a solution selection that has deformation

turned on. Therefore, small deformation theory is used, i.e. displacements of the material

particles are assumed to be much smaller than any relevant dimension of the body, so at each

point of space can be assumed to be unchanged by the deformation.

The results of the equivalent stress, total deformation, and strain energy are presented in

Chapter 4.

3.2.4 Topological Optimization

When meshing is done in Mechanical and loads are applied and evaluated, the topological

optimization can be initiated. All steps in the process necessary to obtain the required results

are explained below: analysis settings, optimization region, objective and response constraints.

3.2.4.1 Analysis Settings

In analysis settings, it is possible to define some input settings to the solver. The default

maximum number of iterations is 500 but, according to the current problem’s objective, this

value was set to 2000. The solver will iterate until it converges or until it reaches the maximum

number of iterations.

The minimum normalized density is set to 0.001 which the program fully complies with, because

for numerical reasons the density of an element cannot be equal to zero.

The convergence accuracy by default is set to 0.1%, but as the objective of this problem is to

minimize the mass this value must be 0.05% or lower. The value chosen was 0.04%. The

topological optimization solver will approach a stationary point where all constraints will be

satisfied within a tolerance of 0.04% of the defined bound.

As explained in section 2.4.3, the penalty factor recommended is p=3 to ensure a good

convergence and therefore that was the value used.


32

3.2.4.2 Optimization Region

The geometry to be optimized must be divided into design and exclusion region. The design

region is the region that will be optimized, and the exclusion region is a fixed geometry and

cannot be optimized by the solver.

In this work, the exclusion region is the wing surface, so the structure maintains the

aerodynamic shape, and the spars, and the design region is the wing interior.

3.2.4.3 Response Constraints

The stress constraints are used to prevent the stresses at any point in the domain to exceed a

stress level greater than half the yield strength of the material. The response constraint will

be von-Mises yield criteria, with a maximum value of 36.5 MPa, which states that yielding occurs

when the von Mises stress σvm equals the yield stress limit σlim. This yielding constraint is

necessary to enforce the assumption of linear elasticity. The von Mises is calculated for each

element by the following equation [44]:

𝜎𝑣𝑚_𝑖 =1

√2√(𝜎𝑖1 − 𝜎𝑖2)

2 + (𝜎𝑖2 − 𝜎𝑖3)2 + (𝜎𝑖3 − 𝜎𝑖1)

2 + 6(𝜎𝑖42 + 𝜎𝑖5

2 + 𝜎𝑖62 ) (3.11)

where σi1-σi6 are the stress components for element i.

During the aircraft mission, the performance could not be affected, and so it is necessary to

add to this problem the maximum deformation criterion. This constraint is applied on the z-

axis, with a correspondent value of 0.1m, which was chosen as being 10% of the wingspan.

3.2.4.4 Objective

Weight reduction of structures is paramount in several industries due to its numerous benefits,

such as lower consumption, performance gain and a reduction of material cost. The most

common objective in topology optimization is to minimize compliance, which is the same as

maximizing the stiffness. Although, in the present case studies the objective of TO problem is

the mass minimization. However, weight reduction is constrained by several mechanical failure

modes.

SIMP method is described above, assuming constant material density, such that minimizing the

mass corresponds to minimizing volume, furthermore, the domain volume is introduced such

that the objective function is normalized.


33

𝐹𝑖𝑛𝑑: 𝑋 = [𝜌1, 𝜌2, … , 𝜌𝑁]𝑇

(3.12)

Min: 𝑚(𝑋)

𝑠. 𝑡.

{

𝐾𝑈 = 𝐹𝑘𝑉𝑎𝑑 = 𝐿𝑎𝑙𝜎𝑣𝑚𝑖

𝜎𝑙𝑖𝑚≤ 1

∑𝜌𝑖�̅�𝑖 ≤ ℎ𝑉0

𝑁

𝑖=1

0 < 𝜌𝑚𝑖𝑛 ≤ 𝜌𝑖 ≤ 1

where 𝑋 is the design variable vector, 𝜌𝑖 design variable of element material density, m is the

element mass, N is the total number of discrete elements, V0 is the initial volume of the design

domain, h desired volume ratio, �̃�𝑖 is the filtered density, i.e. density now represents the

structure, �̅�𝑖 is the element volume after optimization, 𝐾 is the global stiffness matrix, 𝑈 the

global displacement vector, F the external force vector, 𝐿𝑎𝑙 the adjoint load vector, Vad the

adjoint displacement vector, ρmin the minimum limit of element relative density and N the total

number of discrete elements [34, 45]. The element is represented by i.

where 𝜌�̃� is the filtered density, which is found by a weighted average equation:

𝜌�̃� =∑ 𝑤𝑗𝜌𝑗𝑛𝑖𝑗=1

∑ 𝜌𝑗𝑛𝑖𝑗=1

(3.13)

where wj is the weight function, represented as:

𝑤𝑗 = 𝑟𝑓𝑖𝑙𝑡𝑒𝑟 − ‖𝑥𝑗 − 𝑥𝑖‖ 𝑖𝑓 ‖𝑥𝑗 − 𝑥𝑖‖ ≤ 𝑟𝑓𝑖𝑙𝑡𝑒𝑟 (3.14)

where rfilter is a predetermined mesh filter radius that determines the size of the sphere of

influence, as exemplified in Figure 3.7. The weight function decays linearly with distance

between element i and j determined by their respective coordinates xi and xj [44].

Figure 3.7 – Representation of the effect of the density filter on an arbitrary design variable distribution [44].


34

The objective function is approximated by a uniformly convex function, while equality

constraints, by linear functions and inequality constraints by convex functions as well. So, the

optimization problem is replaced by a separable, convex, and nonlinear sub-problem which is

easier to solve.

The sensitivities of the material volume ∑ 𝜌𝑖�̅�𝑖𝑁𝑖=1 with respect to the element densities ρi are

expressed as [34]:

𝜕

𝜕𝜌𝑖∑𝜌𝑖�̅�𝑖

𝑁

𝑖=1

= �̅�𝑖 (3.15)

To ensure the convergence of the solution, one may introduce a filtering function that limits

the vague minimum width of a member (Sigmund and Petersson 1998). The only drawback of

the continuation method is that the number of iterations required to obtain the optimal design

may be several hundred [46]. For example, it is widely used 3x3 parametric low pass filter,

whose impulse response matrix is defined as [47]:

𝐻 = (1

𝑏 + 2)2

[1 𝑏 1𝑏 𝑏2 𝑏1 𝑏 1

] (3.16)

where b corresponds to filter factor, and b Є [1,∞[.

Figure 3.8 presented the importance of b factor in optimization, clarifying with the same

structure to different b approaches.

Figure 3.8 – Influence of filter factor b on the optimal layout. The ground structure consists of 120x40=4800 4-node elements and the volume is restricted to 50% of the design domain [47].


35

Chapter 4

In this chapter different geometries are investigated. First, the study cases used in this work

are described. Afterward, a structural analysis is effectuated, and the results are evaluated, in

order to proceed to TO. Then, the results from TO are analysed and the study case with lower

mass is chosen, which is the main objective of the work. After that, the result obtained in

ANSYS TO is transported to CATIA V5 to do a geometry smoothed, leading to a wing final design.

Finally, a new structural analysis is realized to investigate the stiffness and strength criterions

imposed.

Study Cases

An optimization of a wing was based on the aircraft’s data of Air Cargo Challenge 2011, as

exemplified in Table 4.1, is presented in this chapter. Figure 4.1 illustrates the aerofoil and in

Appendix B there are the aerofoil coordinates. The design must work under certain

requirements, bearing all the loads and should be lightweight.

Four geometries were studied in this work. The wing composition was simplified since the focus

of the study is removing material from the interior of it. So, no dihedral and sweep were

considerate. The proposal wing is rectangular and since the spars are responsible to support

bending loads, the geometries have also elements presenting these structural components.

Table 4.1 – Aircraft’s data on Air Cargo Challenge 2017.

Figure 4.1 – Image of the aerofoil obtained in XFLR5.

The pressure distribution obtained in ANSYS Fluent, as explained in subsection 3.2.2, is used in

all of the following case studies.

Data Value

Maximum weight (take off) [N] 150 Span [m] 2 Chord [m] 0.25

Load factor (maximum) 3


36

4.1 Geometry

The focus of this work is the main wing body structure. The analysis considers only the structural

support, provided by spars and the wing skin. As follows, all the geometries are described below

to a better understanding. Ideally, axisymmetric structures should be made as a continuum

structure, free from any junctions or assembly, for the topology optimization.

4.1.1 First Case

The geometry is composed of a rectangular wing with two perforations, that are destined to

the spars position, as exemplified in Figure 4.2. The perforation intended to spar, at 25% of the

chord, has a diameter of 25mm and the other, at 75% of the chord, has a diameter of 10mm.

The material used is PLA.

Figure 4.2 – Illustration of the wing root.

4.1.2 Second Case

The geometry is similar to the first one, where PLA is also used. However, the secondary spar

is also at the leading edge, as the primary spar, at 10% of the chord. Figure 4.3 illustrates the

second case.



37

4.1.3 Third Case

The geometry, in PLA, is composed of a rectangular wing without spars, at root, it has an

element with a diameter of 25mm, at 25% of the chord, and with a thickness of 1mm. This

element is to represent the connection between the wing and the fuselage, and with the

objective of restricting the existing six degrees of freedom. For better comprehension, Figure

4.4 illustrates the third case.


4.2 Mechanical

4.2.1 Mesh Element Quality

In Figure 4.5 and in Figure 4.6, the mesh and element quality are presented, respectively,

according to the criterion explained in Chapter 3 (3.2.3). Table 4.2 describes the percentage

of elements with quality above 75%.

Figure 4.5 – Illustration of mesh, for the first wing study.

Figure 4.6 – Representation of the element quality, for the first case.


38

As explained in subsection 3.2.2.1, the type of element in ANSYS is automatically generated,

according to the chosen method, which in this work is “Path Conforming Method”, where

tetrahedrons are the method chosen. The software creates a geometry divided into 10-noded

tetrahedron elements, as characterized in Figure 4.7.

Figure 4.7 – 10-noded tetrahedron element [48].

Table 4.2 – Results from the mesh analysis used on different geometries.

Study Cases Type of Element Number of Elements Percentage of elements with

quality above 75%

1 Tet10 216657 75.1% 2 Tet10 230861 75% 3 Tet10 397679 83.4%

After defining the mesh, BCs can be applied, as explained in section 3.2.3.

After the results of elements percentage with quality above 75%, it must be verified that there

is convergence mesh, i.e. a balance between the accuracy of results and the computational

analysis. The point of mesh convergence is the point where the mesh refinement no longer

changes the results obtained. To interpret where mesh refinement is required, ANSYS

percentage stress error helps. This analyse is defined as the stress error energy divided by the

total strain energy. It is possible to define an expression to plot the percentage stress error,

establishing strain energy as ENERGY POTENTIAL and the absolute stress error energy as SERR,

resulting in the following formula:

(SERR/ENERGYPOTENTIAL)×100 (4.1)

For the region of interest, the aim is to have a percentage of stress error below 5% or 10%.

4.2.2 Results

The results are presented below: Figures 4.8 the distribution of equivalent stress is illustrated;

Figures 4.9 represent the total deformation over the wing; and Figures 4.10 show the

percentage of stress error, which is a rigorous way to control the accuracy of the results. In

equivalent stress and deformation images, there are minimum and maximum indicators. Table

4.3 provides the data for the three structural study parameters and the corresponding mass.


39

Figure 4.8 – Distribution of equivalent (von-Mises) stress over the wing, in Pa, where: a) first case, b) second case and c) third case.

Table 4.3 – Results from Mechanical analysis.

4.2.2.1 Equivalent Stress

Relatively to the first case, the maximum equivalent stress of the structure is 92418Pa,

presenting this value at the trailing edge of the wing root. It has also a brittleness of 34659Pa

on the surface around the secondary spar, while the rest of the structure has a value of 3.84Pa.

The second case shows a maximum value at the wing tip, of 52468Pa. As the secondary spar is

at the leading edge, the structure presents a minimum value, 6.5Pa there and at the trailing

edge, while between reaches at 34981Pa. The third case is almost uniform, yielding a minimum

value for the entire wing of 136.8Pa, while the maximum, of 1.44×108, is in the structure that

represents the connection point wing-fuselage. Stress levels were maintained in wing structure

at acceptable levels of specified limit, which is 36.5×106, according to PLA ultimate tensile

strength.

Study Cases

Equivalent Stress [Pa] Total Deformation [m] Strain Energy [J] Mass [kg] Maximum Minimu

m Maximum Minimum Maximum Minimum

1 92418 3.8424 7.2112×10-6 0 7.1124×10-9 3.4334×10-19 6.1055 2 52468 6.4659 1.7548×10-5 0 1.3604×10-7 1.2648×10-18 6.1055 3 1.4355×108 136.77 18.605×10-3 0 7.6812×10-4 4.1474×10-16 6.7391


40

Figure 4.9 – Distribution of deformation over the wing, in m, where: a) first case, b) second case and c) third case.

4.2.2.2 Total Deformation

For the first and second cases the maximum value is at the wing tip, and the increasing

distribution goes from the leading edge to the trailing edge, where the minimum is at the

leading edge. For the third, the maximum value is also at the wing tip, but the increasing

distribution goes from the wing root to the wing tip.


41

Figure 4.10 – Percentage of stress error, where: a) first case, b) second case and c) third case.

4.2.2.3 Percentage of Stress Error

For all the cases the percentage of stress error proves that results are accurate, demonstrating

good mesh quality.

4.3 Topology Optimization

After the results from Mechanical analysis, TO can be accomplished. The results from the TO

are evidenced, according to the parameters described in subsection 3.2.4.

4.3.1 Optimization Region

Figures 4.11, 4.12 and 4.13 shows where the design region and the exclusion region are located.

The design region is illustrated in blue and the exclusion is in red and the wing root is

represented at right of the images and the tip is at left.


42

Figure 4.11 – Representation of exclusion and design regions, for the first case.

Figure 4.12 – Representation of exclusion and design regions, for the second case.

Figure 4.13 – Representation of exclusion and design regions, for the third case.

4.3.2 Results

After setting the analysis parameters, the objective and optimization region defined, the

results can be obtained. In Table 4.4 results from the TO are exemplified and Figures 4.14 and

4.15 illustrate where the removed and retained material are, respectively, for the first case.

Figures 4.16 and 4.17 exemplify in the second case. The third case corresponds to Figures 4.18

and 4.19. In Appendix C is presented for the four cases images illustrating graphics of the

objective convergence, variation of global stress response and variation of displacement

response.

Table 4.4 – Results of the Topology Optimization, to the different study cases.

Study Cases Original Volume [m3]

Final Volume [m3]

Final Mass [kg]

Iteration Number

1 4.9147×10-3 3.9482×10-3 4.8957 6 2 4.9147×10-3 4.1071×10-3 5.0928 6 3 5.4257×10-3 1.9222×10-3 2.3835 231


43

Figure 4.14 – Representation of the removed material, of the first case.

Figure 4.15 – Representation of the retained region, of the first case.

Figure 4.16 – Representation of the removed material, of the second case.

Figure 4.17 – Representation of the retained region, where the tip of the wing is detached, of the second case.


44

Figure 4.18 – Representation of the removed material, of the third case.

Figure 4.19 – Representation of the retained material, of the third case. The image focus on wing’ tip to the interior.

Concerning to analyses, ANSYS TO only support 3D geometries with 20, 10 or 8 nodes. In present

work geometries were defined by 10 nodes, i.e. it has three degrees of freedom at each node:

translations in the nodal x, y and z directions. The elements have plasticity, stress stiffening,

and large strain capabilities. Nevertheless, TO does not support large-deflections effects in

static structural analysis, as referred previously, nonlinear contacts, axisymmetric model when

is defined a global von-Mises stress constraint and local von-Mises stress constraint, and initial

type boundary conditions, i.e. acceleration, standard earth gravity, rotational velocity, and

rotational acceleration.

Having said that, the results are analysed afterward. In the first and second cases, the final

mass is similar, demonstrating that the position of the secondary spar has no influence in the

optimization. Although the objective function in the sixth iteration has converged, the

convergence values for global stress and for displacement were distant from the established

criterions. These results can be observed in Appendix C, in C.1 – First Case and C.2 – Second

Case.

In the third case, with the minimum final mass compared with the other cases, the convergence

value of global stress response was coincident with the defined criterion, while the convergence

value of displacement was too distant from the criterion, as illustrated in Appendix C, in C.3 –

Third Case. According to the figures of the appendix, it is possible to observe that the

convergence value of global stress was from the 12th iteration, approximately, coincident with

the value of global stress criterion. This correspondence is justified due to the maximum


45

structural result on the equivalent (von-Mises) stress is higher than the yield stress limit, and

this could be a possible cause for the optimization model not remove more material from the

structure. However, the local where the maximum was detected was designated previously as

non-space in TO. So even achieving better results, when compared to others, the combined

objective convergence should only stop when the displacement response criterion was

coincident with displacement response convergence.

In Appendix C, Figures C.1, C.3, and C.5 show the objective convergence criterion, which in all

cases is the mass minimization. The objective convergence criterion considers the design

variables, strength, and stiffness, according to equation 3.12. As the objective is to minimize

the mass, in Figure C.1 and C.3, when ANSYS detects an increasing of objective function value

stops the iterations and assume convergence. In the third case, it was different, because the

objective function value in 230th decreases, reaching a value well below the combined objective

convergence criterion, and as in 231th the value become the same the program assumes the

convergence.

During the iterations neither the dynamics of the system nor the topology is physically correct,

due to the stiffness and mass of the geometry change significantly, even so, it converges to a

correct result, both for topology and dynamical behaviour, assuming that the thickness of the

elements of the final result is either one or zero.

4.4 Post-processing and design verification

The results from Topology Optimization can be transferred to the Design Validation System,

which is very accurate for post-processing possibilities. At SpaceClaim, two geometries are

transferred, the geometry before optimization and the other after TO, for providing an easier

post-process.

As the results from the first and second, in terms of final mass, these geometries are excluded

from the post-processing. Although the third geometry has been a final mass too high from the

expected, due to the weight of the UAV being 5kg, post-processing of the geometry is done, in

CATIA, and then a design verification.

The design verification is a test that ensures that the final product fulfils the specified

requirements, under specified operating conditions. In this case, the geometry will be exported

again to the ANSYS Mechanical and will be submitted to a distribution of pressure and loads, to

see if it verifies the strength and stiffness criterions.


46

4.4.1 Final design

A model was created, based on the result from topology optimization for the third case, with

a thick shell of 2mm, as showed in Figure 4.20 and 4.21. From 75% of the chord to the trailing

edge, it is all covered by PLA material.

Figure 4.20 – Representation of the final geometry, as viewed from the side, in CATIA.

Figure 4.21 – Representation of the optimized geometry, from the top, in CATIA.

High stress can be decentralized by adding structural elements, as it was done in the root wing,

between the wing-fuselage connection. Figure 4.22 shows the structural elements and in

Appendix D it is possible to a better perception of elements dimensions. Reducing the stress

concentration factor under static load will increase the fatigue endurance of the component.


47

Figure 4.22 – Representation of the support from the connection between wing-fuselage.

4.4.2 Structural Analysis

Table 4.5 has the data of final design, with respect to von-Mises stress and total deformation

results. Figures 4.23 and 4.24 complete the analyse.

Table 4.5 – Results of the final design, obtained in ANSYS.

Equivalent Stress [Pa] Total Deformation [m] Strain Energy [J] Mass [kg] Maximum Minimum Maximum Minimum Maximum Minimum

9.4252×107 350.88 4.7299×10-2 0 2.2556×10-3 2.4165×10-13 1.5201

Figure 4.24 – Distribution of deformation over the wing, in m.

Figure 4.23 - Distribution of equivalent (von-Mises) stress over the wing, in Pa.


48

The maximum value of equivalent stress is located in the structure where is represented the

spar, as occurred in the mechanical analysis of the third case. Although the maximum value of

equivalent stress is higher from the expected, 36.5×106Pa, is only local, with a small volume.

Unidirectional carbon fibre reinforced plastic (mentioned in 3.2.3.1) can be applied to this

element since bear higher strength compared to PLA. Concerning to deformations, the

maximum value is at the wing tip, however, is less than 10% of the wingspan.


49

Chapter 5

Conclusions and Future Work

5.1 Conclusions

All the proposed tasks were concluded. The most important objective was the TO, and after

different analysis, a lighter structure was proposed, which was obtained through the third study

case.

Firstly, a CFD analysis was executed. The k-epsilon (ε) was chosen. Then, to determine the

performance, structural analyses were performed, where the chosen parameters were: von-

Mises equivalent stress, total deformation, and strain energy. After the results obtained from

the Mechanical, TO was initiated. The results from the equivalent von-Mises stress showed that

the maximum stress created within the body is much smaller, around 0.25% of the limit in the

wing structure imposed than the tensile limits of the materials.

As referred initially, the third case was used to obtain the final design, excluding from this

process the first and second cases due to their final weight. After TO, a 64% reduction in

structural weight was achieved. Following that, a smooth process in CATIA was performed,

resulting in a final mass of 1.5 kg. Nevertheless, this design is susceptible for future TO, since

the final weight is still heavier than the desired one for the required UAV.

As mentioned in Chapter 2, AM is used specially to create complex geometries, without any

obstacle, like tool or moulds barriers as the traditional methods. It was expected that the final

geometry provided by ANSYS TO, was a complex one, but the software created a wing with

thick skin, without any complex structures inside the wing surface. And for this reason, 3D

printing was excluded.

TO achieve stiffness and strength condition, i.e. TO did not create structures that exceeded

the imposed criterions. Either, obtain results where the mass value reduces, although it was

not enough. Concluding, this method was not appropriate for these geometries since the

equivalent stress of the wing structures are below from the imposed limit, 36.5×106Pa.

5.2 Challenges

With the accomplishment of this works some challenges have arisen. The principal challenge

was the computational time, due to be an analysis with 3D geometries. The CFD and TO analysis


50

were fully dependent on the computational time cost, leading to simulations longing for several

days.

During topological optimization was created in geometries some discontinuities and

irregularities as the method remove material from the reference domain of structures. The

phase more challenging was the post-processing, where the geometry obtained was transferred

to SpaceClaim, a CAD software integrated into ANSYS. The mesh created previously is also

transferred and the hard task is to remove it because the transition to tetrahedron elements

to bigger elements creates more discontinuities in geometry, i.e. a face with curvature in some

cases can be transformed in a plate, which in this work cannot happen because affects the

aerodynamic performance. In some cases, it was possible to maintain the curvature of faces,

however, to analyse structurally the optimized geometry it is necessary to create other mesh,

many times above the other which succeed in results with smaller accuracy or non-accuracy.

So, for this reason, CATIA was the software chosen to do the post-processing.

Another challenge was the design verification. A final geometry was created with thickness

variation, this is, the difference in thickness from the root to the wing tip however ANSYS could

not do the structural analysis, due to geometry contacts (Rigid body – maximum contact

stiffness was too big).

5.3 Future Work

The following topics were noted as future work to continue the study of topology optimization

for unmanned aircraft wings:

• A further study will be completed to determine the possibility of using internal

components, like load-bearing structures.

• A further investigation with other software using topology optimization, comparing the

results with the Matlab code written by Ole Sigmund [49].

• Another investigation could be making the aerodynamic and structural study of a 3D

wing. Then, where the parameters are similar the geometry could be turned into a 2D

one, with the objective of making a TO, and then with the resulting geometry, replicate

it in order to obtain again a 3D structure. In this way, computational time is saved, and

complex structures could be obtained.

For all the previous topics AM should be considered.


51

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55

Appendixes

Appendix A

Table A.1 – Results from XFLR5, to a fixed speed of 24 m/s.

Α [º] CL CDi CD Cm V [m/s] XCP L [N]

-5 0,508441 0,011601 0,011601 -0,44856 24 0,2233 42,72124658

-4 0,59088 0,015341 0,015341 -0,46953 24 0,2006 49,64810112

-3 0,673035 0,019601 0,019601 -0,49039 24 0,1834 56,55109284

-2 0,754855 0,024373 0,024373 -0,51113 24 0,17 63,42593652

-1 0,836288 0,029649 0,029649 -0,5317 24 0,1593 70,26826291

0 0,917283 0,035418 0,035418 -0,55209 24 0,1505 77,07378679

1 0,997788 0,041667 0,041667 -0,57227 24 0,1431 83,83813891

2 1,077754 0,048385 0,048385 -0,59223 24 0,1369 90,5572021

3 1,157132 0,055554 0,055554 -0,61192 24 0,1315 97,22685917

4 1,235873 0,063159 0,063159 -0,63134 24 0,1269 103,842993

5 1,31393 0,071183 0,071183 -0,65045 24 0,1229 110,4016543

6 1,391257 0,079605 0,079605 -0,66923 24 0,1193 116,8989782

7 1,467809 0,088406 0,088406 -0,68767 24 0,1161 123,3311834

8 1,543542 0,097564 0,097564 -0,70573 24 0,1133 129,694573

9 1,618413 0,107056 0,107056 -0,7234 24 0,1108 135,9855339

10 1,692381 0,116858 0,116858 -0,74065 24 0,1085 142,2006211

11 1,765405 0,126946 0,126946 -0,75747 24 0,1064 148,3363897

12 1,837449 0,137293 0,137293 -0,77383 24 0,1046 154,3898148

13 1,908473 0,147873 0,147873 -0,78971 24 0,1028 160,3575354

14 1,978444 0,158658 0,158658 -0,80509 24 0,1013 166,2367787

15 2,047328 0,169619 0,169619 -0,81996 24 0,0998 172,0246879


56

Appendix B

Table B.1 – Aerofoil coordinates.

1.00000 0.00715 0.76280 0.09342 0.29573 0.14422

0.99984 0.00726 0.75313 0.09579 0.28601 0.14341

0.99939 0.00757 0.74335 0.09815 0.27643 0.14249

0.99867 0.00801 0.73347 0.10046 0.26698 0.14145

0.99761 0.00858 0.72346 0.10274 0.25764 0.14028

0.99622 0.00932 0.71332 0.10499 0.24841 0.13901

0.99456 0.01021 0.70308 0.10723 0.23933 0.13764

0.99263 0.01124 0.69277 0.10942 0.23039 0.13614

0.99040 0.01239 0.68235 0.11156 0.22158 0.13452

0.98787 0.01369 0.67183 0.11367 0.21289 0.13281

0.98509 0.01513 0.66124 0.11576 0.20435 0.13099

0.98208 0.01669 0.65058 0.11779 0.19597 0.12906

0.97880 0.01833 0.63985 0.11975 0.18773 0.12703

0.97524 0.02010 0.62904 0.12168 0.17962 0.12490

0.97146 0.02199 0.61818 0.12357 0.17167 0.12268

0.96747 0.02397 0.60728 0.12540 0.16389 0.12035

0.96324 0.02601 0.59633 0.12715 0.15625 0.11793

0.95876 0.02814 0.58532 0.12886 0.14876 0.11543

0.95407 0.03036 0.57429 0.13052 0.14143 0.11285

0.94919 0.03263 0.56325 0.13209 0.13429 0.11018

0.94410 0.03492 0.55218 0.13360 0.12729 0.10744

0.93877 0.03727 0.54107 0.13504 0.12046 0.10462

0.93326 0.03967 0.52997 0.13641 0.11380 0.10175

0.92756 0.04208 0.51888 0.13771 0.10732 0.09879

0.92164 0.04448 0.50779 0.13891 0.10101 0.09578

0.91549 0.04691 0.49668 0.14005 0.09486 0.09271

0.90916 0.04937 0.48561 0.14112 0.08889 0.08960

0.90264 0.05182 0.47457 0.14209 0.08312 0.08644

0.89591 0.05425 0.46355 0.14297 0.07752 0.08323

0.88895 0.05668 0.45254 0.14378 0.07208 0.07999

0.88179 0.05914 0.44160 0.14449 0.06685 0.07673

0.87445 0.06160 0.43071 0.14511 0.06180 0.07343

0.86691 0.06405 0.41986 0.14564 0.05694 0.07010

0.85915 0.06652 0.40905 0.14608 0.05226 0.06677

0.85122 0.06900 0.39833 0.14642 0.04777 0.06342

0.84313 0.07147 0.38769 0.14667 0.04349 0.06008

0.83485 0.07393 0.37710 0.14680 0.03939 0.05673

0.82638 0.07640 0.36659 0.14685 0.03548 0.05340

0.81775 0.07888 0.35617 0.14680 0.03177 0.05008

0.80898 0.08133 0.34586 0.14664 0.02826 0.04679

0.80004 0.08377 0.33563 0.14636 0.02496 0.04352

0.79093 0.08621 0.32548 0.14599 0.02184 0.04028

0.78169 0.08864 0.31545 0.14551 0.01892 0.03707

0.77232 0.09105 0.30554 0.14492 0.01622 0.03392

0.01372 0.03081 0.24736 -0.00173 0.91737 0.02816

0.01141 0.02774 0.25868 -0.00041 0.92628 0.02558

0.00932 0.02475 0.27015 0.00097 0.93467 0.02289

0.00744 0.02180 0.28179 0.00239 0.94253 0.02011

0.00577 0.01890 0.29357 0.00385 0.94982 0.01729


57

0.00429 0.01605 0.30551 0.00536 0.95652 0.01450

0.00303 0.01327 0.31761 0.00692 0.96266 0.01180

0.00200 0.01057 0.32986 0.00851 0.96829 0.00920

0.00118 0.00795 0.34226 0.01014 0.97337 0.00672

0.00056 0.00539 0.35480 0.01181 0.97790 0.00443

0.00016 0.00292 0.36748 0.01351 0.98196 0.00234

0.00000 0.00000 0.38031 0.01525 0.98558 0.00044

0.00007 -0.00169 0.39327 0.01701 0.98873 -0.00125

0.00033 -0.00370 0.40638 0.01880 0.99143 -0.00273

0.00083 -0.00554 0.41965 0.02062 0.99374 -0.00396

0.00165 -0.00725 0.43309 0.02243 0.99569 -0.00499

0.00284 -0.00879 0.44667 0.02422 0.99725 -0.00584

0.00445 -0.01020 0.46037 0.02599 0.99842 -0.00646

0.00645 -0.01150 0.47419 0.02773 0.99926 -0.00686

0.00879 -0.01269 0.48814 0.02942 0.99980 -0.00708

0.01143 -0.01375 0.50217 0.03104 1.00000 -0.00715

0.01439 -0.01469 0.51628 0.03260

0.01767 -0.01554 0.53044 0.03410

0.02124 -0.01630 0.54467 0.03553

0.02511 -0.01696 0.55893 0.03687

0.02927 -0.01751 0.57320 0.03813

0.03375 -0.01797 0.58748 0.03934

0.03851 -0.01833 0.60178 0.04045

0.04356 -0.01860 0.61607 0.04147

0.04890 -0.01877 0.63031 0.04239

0.05455 -0.01885 0.64452 0.04325

0.06048 -0.01883 0.65871 0.04401

0.06670 -0.01872 0.67285 0.04465

0.07321 -0.01852 0.68691 0.04518

0.08002 -0.01822 0.70090 0.04563

0.08711 -0.01785 0.71483 0.04594

0.09449 -0.01740 0.72867 0.04608

0.10215 -0.01685 0.74235 0.04606

0.11009 -0.01623 0.75585 0.04590

0.11831 -0.01554 0.76917 0.04558

0.12679 -0.01479 0.78225 0.04509

0.13554 -0.01396 0.79505 0.04446

0.14457 -0.01306 0.80759 0.04372

0.15384 -0.01212 0.81987 0.04286

0.16334 -0.01113 0.83189 0.04186

0.17308 -0.01009 0.84362 0.04074

0.18307 -0.00898 0.85508 0.03950

0.19330 -0.00784 0.86630 0.03811

0.20373 -0.00668 0.87724 0.03652

0.21437 -0.00549 0.88783 0.03474

0.22520 -0.00427 0.89807 0.03277

0.23620 -0.00301 0.90795 0.03058


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Figure C.2 – At left is presented the variation of global stress response and at right is the variation of displacement response.

Figure C.4 – At left is presented the variation of global stress response and at right is the variation of displacement response.

Appendix C

C.1 – First Case

Figure C.1 – Objective convergence vs objective convergence criterion.

C.2 – Second Case



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Figure C.6 - At left is presented the variation of global stress response and at right is the variation of displacement

response.

C.3 – Third Case



60

Appendix D

Figure D.1 – Dimensions from the support geometry of the connection between wing-fuselage.

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